Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-2y &= -1 \\ 9x+y &= 6\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-9x+6}$ Substitute this expression for $y$ in the first equation. $-8x-2({-9x + 6}) = -1$ $-8x + 18x - 12 = -1$ Simplify by combining terms, then solve for $x$ $10x - 12 = -1$ $10x = 11$ $x = \dfrac{11}{10}$ Substitute $\dfrac{11}{10}$ for $x$ back into the top equation. $-8( \dfrac{11}{10})-2y = -1$ $-\dfrac{44}{5}-2y = -1$ $-2y = \dfrac{39}{5}$ $y = -\dfrac{39}{10}$ The solution is $\enspace x = \dfrac{11}{10}, \enspace y = -\dfrac{39}{10}$.